Synchronous chaos in the coupled system of two logistic maps

Synchronous chaos is investigated in the coupled system of two Logistic maps. Although the diffusive coupling admits all synchronized motions, the stabilities of their configurations are dependent on the transverse Lyapunov exponents while independent of the longitudinal Lyapunov exponents. It is shown that synchronous chaos is structurally stable with respect to the system parameters. The mean motion is the pseudo-orbit of an individual local map so that its dynamics can be described by the local map. (C) 2004 Elsevier Ltd. All rights reserved.

Molecular epidemiology of the heterosexual HIV-1 transmission in Kunming, Yunnan Province of China suggests origin from the local IDU epidemic

Molecular epidemiological investigation was conducted among injecting drug users (IDUs) (n = 11) and heterosexuals (n = 15) in Kunming, Yunnan Province of China. HIV-1 genotypes were determined based on the nucleotide sequences of 2.6-kb gag-RT region. The distribution of genotypes among IDUs was as follows: CRF07_BC (5/11) and CRF08_BC (5/11); subtype B' (1/11). Similarly, a majority of Kunming heterosexuals (14/15) were infected with CRF07_BC (4/15), CRF08_BC (6/15), or subtype B' (4/15), known to predominate among IDUs in China. This contrasts with trends in the coastal regions of China and surrounding southeastern Asian countries, where CRF01_AE predominates among heterosexuals. The heterosexual HIV-1 epidemic in Kunming thus appears to derive from the local IDU epidemic. Of note, subtype B' was the most prevalent strain among heterosexuals before 1997, while CRF07_BC and CRF08_BC became predominant in 2002, indicating a transition of HIV-1 genotype distribution between the early and the more recent samples from Kunming heterosexuals.

Logistic回归分析在厚颌鲂生活史类型研究中的应用

以34种中国淡水鱼类和近海鱼类的生态参数为基础,建立logistic回归模型。利用该模型研究长江上游龙溪河厚颌鲂的生活史类型,然后用平衡产量模型进行验证,并探讨合理开发龙溪河厚颌鲂种群资源的渔业管理措施。结果表明:logistic回归模型估算出厚颌鲂属于k选择鱼类的概率为13%,判别标准为29%,因此厚颌鲂应该属于r选择鱼类;Beverton-Holt产量模型分析结果显示厚颌鲂平衡产量曲线与典型的r选择鱼类尖头塘鳢极为类似;捕捞死亡系数和起捕年龄的变化对产量曲线有显著影响,因此限制捕捞量和网目大小是控制过

Logistic Map耦合格子模型模拟环带

本论文采用Logistic Map耦合格子模型对高聚物中特有的环带球晶进行了模拟，所得到的模拟结果与实验结果吻合较好。同时，研究结果能够对实验制备环带球晶样品提供可靠的理论指导。 首先，我们对Logistic Map耦合格子模型及模型中的两个模拟参量μ和ε进行分析，同时结合实验中各种实验条件对聚合物结晶行为的影响，认为Logistic Map的动力学特征与聚合物结晶行为非常相似，并且参量μ与实验中的结晶温度相关，即随温度的升高而减小，而参量ε与实验中影响扩散的因素有关，即随温度的升高而增大、随分子量的增大而减小，并且随样品厚度的增大而增大。我们对模型的整个参数空间进行计算，得到了可以形成环带球晶形貌的参数范围，通过进一步研究发现环带图案的带宽随参量μ的增大而变窄，随参量ε的增大而变宽。上述研究结果与实验中带宽随实验条件的变化规律是一致的。 在得到环带图案的基础上，我们又进一步计算得到了靶状和螺旋状形貌的参量μ和ε的具体取值范围。通过改变μ和ε的参数取值，模拟了环带球晶形貌由靶状过渡到螺旋状的过程，即靶状图案的环带由外层向内层逐渐断裂成较短的条带结构，所有的条带结构呈现出以空间某处为中心团聚在一起的形貌；随后，这种“团聚”的形貌逐渐消失了，空间中小的条带结构的排列呈无序状态。随着参数的进一步变化，短的条带结构变成较长的带状结构，并且这些带状结构的边缘逐渐发生卷曲，最终形成了螺旋状图案。我们还考察了系统初值和耦合方式对上述图案的影响，结果发现，形成环带球晶的参数范围对系统初值没有明显的依赖性，然而靶状和螺旋状图案的分布受初值的影响较大。此外，发现只有采用交替耦合、并考虑长程耦合作用的Logistic Map耦合格子模型才可以得到环带球晶图案。 为了更好地与实验结果进行对比，我们利用Logistic Map耦合格子模型对二维空间中的几种受限体系进行了模拟。（一）对温度梯度场中的环带球晶进行模拟，发现环带球晶在低温处较易成核，向高温处生长，并且，高温处环带的带宽比低温处宽。（二）对格子宽度受限情况进行了模拟，发现随着受限方向的宽度越来越窄，球晶尺寸逐渐变小，相邻两个环带球晶碰撞产生的界线变短，三个相邻环带球晶所形成的界线的交汇点减少。（三）研究了受限边界上的成核作用对狭长格子中环带球晶的影响，结果发现，随着受限边界上成核点密度的不断增加，其形貌转变分为三个不同阶段：①当成核密度稍有增大时，环带球晶数量增加，直径变小；②继续增大边界成核密度，使得大量晶层从受限边界向格子内生长，导致环带球晶的数量减少，直径也减小；③当成核点增加到一定程度时，整个空间中只有极少数由格子内部成核生长且直径非常小的环带球晶，而占主导地位的是由成核点垂直于受限边界生长出的穿透晶层。这些模拟结果均与实验结果相符合。 我们将Logistic Map耦合映象格子模型发展到三维空间格子中，得到了与环带球晶形貌一致的图案，并且其带宽随模拟参量μ的增大而变窄，随ε的增大而变宽。这一规律性结果与二维正方格子的模拟结果是一致的。这一部分的研究结果还表明，边界条件和格子尺寸对模拟结果有显著的影响，周期性边界条件导致在小体积立方格子中只能得到靶状图案；而当格子尺寸很大时，可以得到螺旋状环带球晶的图案。最后，通过调节垂直于薄膜平面方向上的格子数来研究薄膜厚度对环带图案带宽的影响，发现环带的带宽随厚度的增加而变宽，这与实验中环带球晶的带宽随样品厚度的增加而变大的结论是一致的。

崔—Lawson模型与logistic方程的比较研究

本文对崔—Lawson模型与logistic方程进行了比较，指出了以营养动力学为基础的崔—Lawson模型关于生物物种与营养环境之间关系的内涵思想，从而揭示了崔—Lawson模型比logistic方程之所以深刻的关键所在。本文通过对棕色固氮菌的菌体培养实验，系统地验证了以营养动力学为基础的崔—Lawson模型思想，并且对实验数据分别进行了崔—Lawson模型及logistic方程拟合。对两个模型拟合出的残差平方和进行了比较。证实崔—Lawson模型比logistic方程更适合于对实验资料的描述。并且随着营养水平逐渐降低，logistic方程拟合的残差平方和逐渐减小，从而说明只有在营养水平低的情况下，才适合用logistic方程，而通常情况下，用logistic方程是不合适的。

利用logistic模型对MODIS数据进行湿地提取

MODIS是近年来较常用于宏观土地利用/土地覆盖的一种遥感数据来源。为了克服MODIS空间分辨率的限制,在建立提取模型的时候使用了多期遥感数据,并且加入了地形辅助数据。Logistic模型是一种非线性的回归分析模型,它通常是用于预测和判定未知单元的类别属性。先划出训练样区,计算出湿地分布与各因子之间的关系式,进而得到湿地分布概率图,选取一定的阈值(0.5),最终提取出湿地。研究结果显示,Logistic模型用于遥感分类,分类精度高于最大似然法。另外,加入了地形因子(dem,slope,tpi)后,分类精度得到明显的提高。

The study of banded spherulite patterns by coupled logistic map lattice model

Banded spherulite patterns are simulated in two dimensions by means of a coupled logistic map lattice model. Both target pattern and spiral pattern which have been proved to be existent experimentally in banded spherulite are obtained by choosing suitable parameters in the model. The simulation results also indicate that the band spacing is decreased with the increase of parameter mu in the logistic map and increased with the increase of the coupling parameter epsilon, which is quite similar to the results in some experiments. Moreover, the relationship between the parameters and the corresponding patterns is obtained, and the target patterns and spiral patterns are distinguished for a given group of initial values, which may guide the study of banded spherulite.

Simulation of Banded Spherulite Patterns by Coupled Logistic Map Lattice Model in Three Dimensions

Banded spherulite patterns are simulated in three dimensions by means of a Coupled Logistic map lattice model. The patterns obtained by numerical calculation are consistent with those in experiments. The simulation results also indicate that the hand spacing is decreased with the increase of parameter mu in the Logistic map and increased with the increase of the coupling parameter e for cube lattices, and increased with the increase of the thickness of the lattice for polymer film, which is quite similar to the results in some experiments. Spiral pattern in three dimensions is also shown in this paper, which helps us understand the form of banded spherulite in polymers.

SARS流行预测分析

表面上突如其来的SARS本质上却有极规律的内在发展演化机制,遵从初始缓慢增长、加速、减速和稳定终止四个阶段总体道路,自然和社会生活领域众多事件演化都符合这一规律,因而可以运用广义的Logistic生长模型进行描述.基于先期流行的广东SARS感染病例数据,以及尚未结束的北京、全国2003年SARS流行统计数据,借助于最优化分析技术,运用广义的Logistic生长模型对该事件演化特征参量进行了辨识;在此基础上,又借助于广义生长模型的特例--Gompertz函数进行了演化过程的预测,并与其他生长模型结果进行了比较.研究表明,生长模型模拟结果均与实际数据有很好的一致性,可以用来预测事件的发生演化过程,此次SARS事件堪称生长模型的经典实例.

Control dynamics of severe acute respiratory syndrome transmission

Severe acute respiratory syndrome (SARS) is a serious disease with many puzzling features. We present a simple, dynamic model to assess the epidemic potential of SARS and the effectiveness of control measures. With this model, we analysed the SARS epidemic data in Beijing. The data fitting gives the basic case reproduction number of 2.16 leading to the outbreak, and the variation of the effective reproduction number reflecting the control effect. Noticeably, our study shows that the response time and the strength of control measures have significant effects on the scale of the outbreak and the lasting time of the epidemic.

Wavelike patterns in one-dimensional coupled map lattices

We investigate the existence of wavelike solution for the logistic coupled map lattices for which the spatiotemporal periodic patterns can be predicted by a simple two-dimensional mapping. The existence of such wavelike solutions is proved by the implicit function theorem with constraints. We also examine the stabilities of these wave solutions under perturbations of uniform small deformation type. We show that in some specific cases these perturbations are completely general. The technique used in this paper is also applicable to investigate other space-time regular patterns.